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Need Spiral Cutting Advice

I am trying to cut a spiral into 1/4" plywood. I have the layout OK, but trying to get a smooth Arc is very tough. Both the jigsaw and bandsaw are prone to wandering. Does anyone know of how to cut a smoother cut? Maybe a roto zip tool would be better but how do you keep the cut arc even?The spiral is 1" wide and starts at 12" in dianeter.THx

Thx for the answer but sanding is impossible because the spiral is 12" in external diameter and spirals inwards on a 1" wide strip. It's a spiral "drain" part for a kids marble maze project which is quite hard to make. Lots of compound miters, etc